Reduction of second-order non-linear distortion in a wideband communication system

ABSTRACT

A system has a plurality of non-linear circuit stages and an intervening linear circuit stage. An input signal is provided to a first non-linear circuit stage, and from the first non-linear circuit stage, to the linear circuit stage. The first non-linear circuit stage applies a second-order distortion to the input signal and provides the resulting signal to the linear circuit stage. The resulting signal that is output from the linear circuit stage is inverted with respect to the input signal and suitably linearly processed (attenuated or amplified). This signal is then provided to a second non-linear circuit that applies a second-order distortion and outputs a signal that has an overall reduction in second-order distortion.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. application Ser. No.15/597,937 filed on May 17, 2017, entitled “REDUCTION OF SECOND-ORDERNON-LINEAR DISTORTION IN A WIDEBAND COMMUNICATION SYSTEM,” whichapplication is incorporated herein by reference.

BACKGROUND

Radio frequency (RF) amplifiers are used in a variety of conventionalapplications. As an example, RF amplifiers are frequently used in datacommunications in order to increase the range or signal quality of datasignals communicated through a network. Ideally, a RF amplifier islinear such that its output signal varies proportionally to its inputsignal. However, in reality, the transfer function of all RF amplifierscontains some non-linear terms, and these introduce some harmonic orintermodulation distortion in the output signal. In a narrow-bandcommunication system, second order distortion falls outside thefrequency band of interest, and can be removed by filtering. However,filtering is inappropriate where the instantaneous bandwidth is greaterthan an octave such that the second order harmonics or intermodulationproducts fall in band.

One solution that has been used to reduce second order harmonicdistortion in wideband systems involves the use of multiple amplifiersarranged in a parallel, balanced or anti-phase configuration such thatasymmetrical distortion in each amplifier produces symmetricaldistortion in the output signal, thereby cancelling the effects ofsecond order harmonics. However, the use of a parallel path foramplifiers is not always possible or convenient, and techniques forreducing second order distortion in the output of an amplifier withoutrequiring an additional amplifier in a parallel, anti-phase arrangementare generally desired.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present, its nature and variousadvantages will be more apparent upon consideration of the followingdetailed description, taken in conjunction with the accompanyingdrawings in which:

FIG. 1A depicts an illustrative functional diagram of linear andnon-linear circuit stages for removal of second order distortion inaccordance with some embodiments of the present disclosure.

FIG. 1B depicts an illustrative functional diagram of linear andnon-linear circuit stages disclosure for removal of second orderdistortion in accordance with some embodiments of the presentdisclosure.

FIGS. 2A and 2B depict illustrative schematic diagrams and associatedsignals for systems for removal of second order distortion in accordancewith some embodiments of the present disclosure.

FIGS. 3A and 3B depict illustrative schematic diagrams for circuits forapplying a gain and removing second order distortion in accordance withsome embodiments of the present disclosure.

FIG. 4 depicts an illustrative flow chart for a method of removingsecond order distortion in accordance with some embodiments of thepresent disclosure.

FIG. 5 depicts an illustrative flow chart for a method of removingsecond order distortion in accordance with some embodiments of thepresent disclosure.

FIG. 6 depicts an illustrative block diagram of a communication systemin accordance with some embodiments of the present disclosure.

FIG. 7 depicts an illustrative block diagram of a remote unit of adistributed antenna system in accordance with some embodiments of thepresent disclosure.

FIG. 8 depicts an illustrative block diagram of an optical module inaccordance with some embodiments of the present disclosure.

DETAILED DESCRIPTION

The present disclosure generally pertains to systems and methods forreducing second order non-linear distortion in electronic circuits suchas gain circuits (e.g., amplifiers or other circuits that apply anon-linear transfer function including a second-order term to an inputsignal). In one embodiment, a system includes a plurality of circuitstages (e.g., one or more circuit elements that process an incomingsignal) that process a signal, for example, to apply an overall gain tothe signal. In an embodiment, some of the circuit stages are non-linearcircuit stages (e.g., they have a non-linear transfer function includinga second order term) and other circuit stages are substantially linear(e.g., they apply a proportional, also known as “first order”,modification to an input signal). In some applications, it may benecessary to use components that apply non-linear processing to an inputsignal, while nonetheless limiting certain types of non-lineardistortion. For example, in certain systems harmonics may interfere withother signals of interest, but a non-linear component that creates suchharmonics (e.g., an amplifier) may nonetheless be desirable for aparticular application (e.g., due to power consumption, size, cost,etc.).

As described herein, the various circuit stages may be configured andcoupled such that desired processing is performed while substantiallyeliminating undesired second-order-distortion. In an embodiment, a firstnon-linear circuit stage, a linear circuit stage, and a secondnon-linear circuit stage may be coupled in series. The first non-linearcircuit stage may receive an input signal, process the signal in amanner that adds a non-linear component to the input signal (e.g.,second order processing that results in a plurality of additional secondorder signal components) and output the processed signal to the linearcircuit stage. The linear circuit stage may process the received signalin a linear manner (e.g., first order processing) and provide its outputsignal to the second non-linear circuit stage. The collective processingof the first non-linear circuit stage and the linear circuit stage mayresult in the output signal from the linear circuit stage having asubstantially unity gain and being inverted when compared to the inputsignal to the first non-linear circuit stage. This output signal fromthe linear circuit stage is provided to the second non-linear circuitstage, which has at least some substantially similar characteristics(e.g., second order distortion) to the first non-linear circuit stage.

In an embodiment, both of the non-linear circuit stages are identicalgain stages, e.g., having substantially identical components andfunctionality such that a gain is applied to an incoming signal to eachof the non-linear circuit stages in a substantially identical manner(e.g., an identical first order gain and second order distortion areapplied by each of the non-linear circuit stages). In order to maintainthe substantial unity gain of the first non-linear circuit stage andlinear circuit stage, the linear circuit stage may be an attenuationstage that attenuates the first order components of the signal that isoutput from the first non-linear circuit stage in accordance with thegain of the first non-linear circuit stage, resulting in an overallunity gain. The inversion of the first non-linear circuit stage and thelinear circuit stage may occur at a variety of points within the seriescircuit between the output of the first non-linear circuit stage and theinput of the second non-linear circuit stage. The gain applied by thesecond non-linear circuit stage may result in an overall first ordergain applied as compared to the input signal. Undesired second ordercomponents may be substantially eliminated from the signal that isoutput from the second non-linear circuit stage, as described herein.

In an embodiment, a first gain stage may be a first non-linear amplifierthat provides a gain (e.g., at least a first and second order transferfunction) to the signal. The output signal from the amplifier may bepassed through an inverter and a linear attenuator that provides acumulative loss (first order negative gain) that is substantiallysimilar to the first order gain applied by the first amplifier. Forexample, the attenuator may have a loss that is the same as the gain ofthe first amplifier. The resulting signal that is output from theattenuator may be inverted and have a unity gain with respect to theinput signal to the amplifier. The amplifier may also add some secondand higher order components to the input signal that are not removed bythe linear attenuator. The signal output from the attenuator may beprovided to a second gain stage which may be a second non-linearamplifier that provides a gain (e.g., at least a first and second ordertransfer function) to the signal. Although the second amplifier mayapply a second order distortion to the signal, the second ordercomponents of the output signal may be substantially cancelled, based onthe inversion and second order components of the first amplifier,attenuator, and inverter. The resulting signal may have the desiredfirst order gain with second order distortion substantially removed fromthe signal.

FIG. 1A depicts an illustrative functional diagram of linear andnon-linear circuit stages for removal of second order distortion inaccordance with some embodiments of the present disclosure. Althoughparticular functional blocks are depicted as being configured in aparticular manner in FIG. 1A, in an embodiment the circuitry of FIG. 1Amay include a first non-linear circuit stage 11 in series with a linearcircuit stage 12 and a second non-linear circuit stage 13.

A non-linear circuit stage 11 may include one or more suitable circuitelements that modify an input signal to the non-linear circuit stage ina non-linear manner, e.g., by applying second, third, and/or higherorder modifications to the incoming signal. The non-linear circuit stage11 may also modify the incoming signal in a linear manner. Components ofa non-linear circuit stage may include components such as amplifiers,electrical-to-optical and optical-to-electrical converters, etc. Inaddition, linear components that modify an input signal in a manner thatis substantially first order only (e.g., inverters, baluns,transformers, matching components, attenuators etc.) may be includedwithin the non-linear circuit stage 11 as long as the output signal hasalso been modified in a non-linear manner within the non-linear circuitstage 11.

A linear circuit stage 12 may be connected in series with the non-linearcircuit stage 11 (e.g., either directly connected or including one ormore intervening circuit elements) to receive the signal that is outputfrom the non-linear circuit stage 11, or in some embodiments, a signalthat is substantially similar to this output signal (e.g., based on oneor more intervening circuit elements). In an embodiment, the non-linearcircuit stage may include one or more suitable circuit elements thatmodify an input signal in a manner that is substantially first orderonly. For example, the linear circuit stage 12 may include one or morecomponents such as inverters, baluns, transformers, matching components,attenuators, etc. When combined with the processing of the non-linearcircuit stage 11, the output signal from the linear circuit stage 12 maybe inverted with respect to the input signal to the linear circuit stage12. Moreover, when combined with the processing of the non-linearcircuit stage 11, the output signal from the linear circuit stage 12 mayhave an overall gain or loss such that that the overall objective ofsubstantially symmetrical waveform distortion is achieved from theentire signal chain including non-linear circuit stage 13. Based on thenon-linear circuit stage 11, the signal that is output from the linearcircuit stage 12 may also include the non-linear signal components thatwere introduced at non-linear circuit stage 11, with the non-linearcomponents being inverted with respect to the original non-linearcircuit stage 11.

A non-linear circuit stage 13 may be connected in series with thenon-linear circuit stage 11 and linear circuit stage (e.g., eitherdirectly connected or including one or more intervening circuitelements) to receive the signal that is output from the linear circuitstage 12, or in some embodiments, a signal that is substantially similarto this output signal (e.g., based on one or more intervening circuitelements). Non-linear circuit stage 13 may include one or more similarnon-linear circuit elements that are found in non-linear circuit stage11. The non-linear circuit stage 13 may also modify the incoming signalin a linear manner.

In an embodiment, the non-linear circuit stage 13 may includesubstantially similar processing to non-linear circuit stage 11 (e.g.,based on identical or functionally similar components) such that firstorder gain and higher order distortion of the non-linear circuit stage11 and non-linear circuit stage 13 are substantially identical. As aresult of the combined processing of the non-linear circuit stage 11,linear circuit stage 12, and non-linear circuit stage 13, the outputsignal may undergo desired processing (e.g., applying a gain by anamplifier that introduces second order distortion) while the outputsignal is substantially free of second order distortion components.

FIG. 1B depicts an illustrative functional diagram of linear andnon-linear circuit stages for removal of second order distortion inaccordance with some embodiments of the present disclosure. FIG. 1Bdepicts a first non-linear circuit stage 11, a linear circuit stage 12,and a non-linear circuit stage 13. In an embodiment, each of thenon-linear circuit stages may be gain (or amplifier) stages (e.g.,active gain stages or passive stages) and the linear circuit stage maybe an attenuation stage, although similar processing may be performed indifferent embodiments using inverting amplifiers or electro-opticaltransducers, etc. In one embodiment, each of the non-linear circuitstages 11 and 13 may be substantially similar, e.g., may have identicalor functionally similar components that apply substantially identicalfirst order and higher order transfer functions (e.g., first order gainand second order distortion) to an input signal. Linear circuit stage 12may be inverting and may apply a first order attenuation that issubstantially identical to the first order gain of the non-linearcircuit stages 11 and 13, such that an overall first order gain or lossfrom the first non-linear circuit stage 11 and the linear circuit stage12 is a substantially unity gain. However, in other embodiments, thenon-linear circuit stages 11 and 13 may be substantially different,e.g., may have different components that apply different first order andhigher order transfer functions (e.g., first order gain and second orderdistortion) to an input signal.

In an embodiment, the output (y) of the non-linear circuit stage 11 canbe expressed in terms of the stage's input (x) according to thefollowing equation, assuming that the signal is distorted by (or thegain applied to the signal contains) only second order harmonicdistortion (i.e., neglecting higher-order distortion that may bepresent), with α₁ representing a first order gain and β₁ representing asecond order gain:

y=α ₁ x+β ₁ x ²  (1)

This signal is provided to the linear circuit stage 12. If it is assumedthat the linear circuit (or attenuation) stage 12 is linear, that theattenuation factor is 1/α₂, and that the linear circuit (or attenuation)stage 12 inverts the received signal y, then the output (z) from thelinear circuit stage 12 (or the input (z) to the non-linear circuit (oramplifier) stage 13) can be expressed as follows:

z=−y/α ₂  (2)

This output signal (z) is provided to the non-linear circuit stage 13.If the non-linear circuit (or amplifier) stage 13 has a first order gainα₃ and second order gain β₃ the output (w) of the non-linear circuit (oramplifier) stage 13 can be expressed in terms of its input (z) fromlinear circuit (or attenuation) stage 12 according to the followingequation.

w=α ₃ z+β ₃ z ²  (3)

Substituting Equation (1) into Equation (2) yields the followingequation for the output of the linear circuit stage 12:

z=−(α₁ x+β ₁ x ²)/α₂  (4)

In an alternate embodiment, where α₁=α₂=α₃=α and β₁=β₃=β, substitutingEquation (1) into Equation (2) yields the following equation for theoutput of the linear circuit stage 12:

z=−x−(β/α)x ²  (4A)

Then, substituting Equation (4) into Equation (3) yields the followingequation for the output of the non-linear circuit stage 13

w=−α ₃(α₁ x+β ₁ x ²)/α₂+β₃(α₁ x+β ₁ x ²)²/α₂ ²  (5)

In the alternate embodiment, where α₁=α₂=α₃=α and β₁=β₃=β, substitutingEquation (4A) into Equation (3) yields the following equation for theoutput of the non-linear circuit stage 13

w=α(−x−(β/α)x ²)+β(−x−(β/α)x ²)²  (5A)

Equation (5) simplifies to the following Equation (6):

w=−α ₃α₁ x/α ₂−α₃β₁ x ²/α₂+β₃α₁ ² x ²/α₂ ²+β₃β₁ ² x ⁴/α₂ ²+2α₁β₃β₁ x²/α₂ ²  (6)

It is possible to cause the second-order term to cancel in Equation (6)if the following condition is true:

−α₃β₁/α₂+β₃α₁ ²/α₂ ²=0  (7)

This can be rearranged as shown:

β₃/α₃*α₁/α₂=β₁/α₁  (8)

In the alternate embodiment, where α₁=α₂=α₃=α and β₁=β₃=β, Equation (5A)simplifies to the following Equation (6A), in which the second orderterms cancel at the output of the non-linear circuit stage 13:

w=−αx+(2β²/α)x ³+(β³/α²)x ⁴  (6A)

One configuration of the alternate embodiment that results in β₁=β₃ andα₁=α₂=α₃ is when the two amplifier stages are identical and theattenuation has the same loss (in dB) as the linear gain of eitheramplifier (in dB). In this configuration, the chain of stages 11-13 is“linearized” with respect to the second order non-linearity. The chainof stages 11-13 may exhibit higher order (e.g., third and fourth order)intermodulation products, but not second order intermodulation products.

More generally, referring back to the discussion of Equations 5-8, thefraction β/α can be thought of as being the second-order distortionrelative to the linear gain of the amplifier stage, referred to itsoutput. If the amplifiers have identical relative characteristics, whereβ₃/α₃=β₁/α₁, it follows that cancellation will still occur when α₁=α₂even when α₁≠α₃. For example, a high-gain input stage and a lower-gainoutput stage can still be arranged to achieve second-order cancellation,provided that they distort in the same way.

In the extreme case where the two amplifiers are completely different,such that β₃/α₃≠β₁/α₁, second-order cancellation can still be achievedby selecting the correct value of α₂:

α₂=β₃α₁ ²/(β₁α₃)  (9)

The inter-stage attenuation, characterized by equation (2), is assumedto contain a signal inversion. It is clear from equation (9) that anequivalent outcome would be achieved if any of β₃, β₁, or α₃ containedan inversion instead. This may be conveniently achieved in someembodiments through appropriately-connected differential devices orcomponents.

FIGS. 2A and 2B depict illustrative schematic diagrams and associatedsignals for systems for removal of second order distortion in accordancewith some embodiments of the present disclosure. In the embodiment ofFIGS. 2A and 2B, an overall RF gain stage 54 includes a non-linearcircuit stage 11 that is implemented as a gain stage 75, a linearcircuit stage 12 that is implemented as an attenuation stage 76, and anon-linear circuit stage 13 that is implemented as a gain stage 81. Thegain stage 75, attenuation stage 76, and gain stage 81 are all coupledin series.

In an embodiment, the gain stage 75 has at least one amplifier 80 (e.g.,RF power amplifier) that is configured to receive and apply a gain to anelectrical signal. Note that the gain stage 75 may have any number ofcomponents (e.g., amplifiers, optical converters, etc.) that arearranged to provide a desired gain (G) to the signal received by thegain stage 54. As an example, the gain stage 75 may have a plurality ofamplifiers 80 connected in series such that each amplifier 80 providesan incremental gain to the received signal in order to achieve anoverall desired first order gain (G). The amplifier(s) may also modifythe input signal in a non-linear manner, for example, by providing asecond order distortion to the input signal. In other embodiments, thegain stage 75 may have other arrangements.

The attenuation stage 76 is coupled to the gain stage 75 and isconfigured to attenuate the signal output by the gain stage 75. In someembodiments, the attenuation stage 76 substantially removes the gainapplied to the signal by the gain stage 75 (e.g., based on a first orderloss of attenuation stage 76 that is substantially identical to thefirst order gain of the gain stage 75). The attenuation stage 76 may beimplemented with any suitable device or devices that apply attenuation(loss) to the gain stage 75 output signal in a manner that issubstantially similar to the gain applied by the gain stage 75. Examplesinclude an attenuator (e.g., attenuator 79), coaxial cable runs, one ormore laser devices of electrical-to-optical or optical electricalconverters, optical fiber runs, etc. The attenuation stage 76 may alsobe configured to perform other processing on the signal as may bedesired. As an example, the attenuation stage 76 may perform inversionof a signal as described herein with regard to FIGS. 2A and 2B, suchthat the output of the attenuation stage 76 is inverted with respect tothe incoming signal. The inversion may be implemented with any suitablecomponent or components that output a signal having substantiallyidentical amplitude and opposite phase from the input signal, such asinverter 77, transformers, or crossover of differential connections. Inother embodiments, the attenuation stage 76 may provide other types offunctions.

The attenuator 79 is configured to attenuate the signal output by thegain stage 75 before such signal reaches the gain stage 81. In someembodiments, the attenuator 79 attenuates the signal by substantiallythe same amount that the gain stage 75 amplifies the signal. That is,the attenuator 79 substantially removes the first order gain (G)provided by the gain stage 75. Thus, in some embodiments, the signallevel input to the gain stage 81 is substantially similar to the signallevel input to the gain stage 75, with the signal inverted based on theoperations performed at gain stage 75 and inverter 77, and including ahigher order component or components based on the non-linear processingof gain stage 75.

The gain stage 81 has at least one amplifier 80 that is configured toreceive and apply a gain to the electrical signal received by the gainstage 81. In an embodiment, the gain stage 81 may provide substantiallyidentical processing as the gain stage 75 (e.g., based on identical orfunctionally similar components). Note that the gain stage 81 may haveany number of amplifiers that are arranged to provide a first order gain(G) to the signal as well as higher order gains. As an example, the gainstage 81 may have a plurality of amplifiers 88 (e.g., RF poweramplifiers) connected in series such that each amplifier 88 provides anincremental gain to the received signal in order to achieve an overalldesired gain characteristics. In other embodiments, the gain stage 88may have other arrangements. As an example, each gain stage 75 and 81may have a single respective amplifier.

In an embodiment, the characteristics of the gain stage 81 aresubstantially similar to the characteristics of the gain stage 75 suchthat the gain stage 81 provides substantially the same first order gain(G) and higher order gain(s) as the gain stage 75. In some embodiments,the same type (e.g., same model number) of amplifier or amplifiers areused to implement both gain stages 75 and 81. Thus, like the gain stage75, the gain stage 81 applies a gain (G) to its input signal such thatthe output signal has a greater amplitude relative to the input signalto the stage. However, the signal that is input to the second gain stage81 is inverted with respect to the original signal input to gain stage75, and includes inverted higher order (e.g., second order) componentsbased on the second order processing of gain stage 75. As a result,second order components may be substantially cancelled from the outputsignal of non-linear circuit stage 81. In some embodiments, other higherorder signal components (e.g., third and fourth order signal components)may remain in the signal in whole or in part (e.g., based on thecomponents being substantially reduced in amplitude or based on thosecomponents not interfering with relevant frequency bands).

FIGS. 2A and 2B also depict a portion of an input signal being processedby the gain stage 75, attenuation stage 76, and gain stage 81. Therelative location of each of the signal portions corresponds to an inputor output signal of a circuit element of the embodiments of FIGS. 2A and2B. An input signal 90 has relative amplitude and is depicted as aninput sinusoid, although it will be recognized that a signal having anysuitable waveform may be provided to the gain stage 75. The output ofgain stage 75 may correspond to signal 92. In the depictions of FIGS. 2Aand 2B, a gain has been applied to the input signal 90. Moreover, in asimplified depiction the signal is depicted as undergoing a “clipping”based on the specifications of the amplifier 80 of the gain stage andthe introduction of higher order (e.g., second order) signal components.

The output signal 92 may be provided to attenuation stage 76, which inthe embodiment of FIGS. 2A and 2B, may include an inverter 77 and anattenuator 79. In the embodiment of FIG. 2A, the inverter 77 isconfigured to invert the signal output by the gain stage 75, with anoutput of inverter 77 depicted as signal 94A. FIG. 2A shows the outputsignal after it has been inverted by inverter 77, with a substantiallyidentical peak-to-peak amplitude as signal 92. As shown by FIG. 2A, thesignal 94A output by the inverter 77 has a clipped trough correspondingto the clipped peak of signal 92, and the signal 94A has a positive peakcorresponding to the negative trough of signal 92. Note that theinverter 77 may be located in the circuit at any point between the gainstages 75 and 81, as described herein. Further, it is possible for theinverter 77 to be integrated into another device for performing anotherfunction. As an example, some amplifiers are designed to invert signalssuch that, if desired, a single electrical device could be used toimplement an amplifier 80 and the inverter 77.

The signal 94A is provided from inverter 77 to attenuator 79. Attenuator79 applies a first order loss to signal 94A that is substantiallyidentical to the first order gain applied by amplifier 80. However,attenuator 79 does not apply significant higher order modifications tothe signal 94A, such that while the peak-to-peak amplitude of the signal96 is reduced with respect to the signal 94A, the waveform shape issubstantially unchanged. The resulting signal 96 may have a peak-to-peakamplitude that is substantially unchanged with respect to the inputsignal 90, with inverted higher order signal modifications based on theoperations of the amplifier 80 and inverter 77.

In the embodiment of FIG. 2B, the attenuator 79 is configured to apply afirst order loss to signal 92 that is substantially identical to thefirst order gain applied by amplifier 80. However, attenuator 79 doesnot apply significant higher order modifications to the signal 92, suchthat while the peak-to-peak amplitude of the signal 94B is reduced withrespect to the signal 92, the waveform shape is substantially unchanged.The resulting signal 94B may have a peak-to-peak amplitude that issubstantially unchanged with respect to the input signal 90.

The inverter 77 is configured to invert the signal output by theattenuator 79, with an output of inverter 77 depicted as signal 96, withinverted higher order signal modifications based on the operations ofthe amplifier 80 and inverter 77. FIG. 2B shows the output signal afterit has been inverted by inverter 77, with a substantially identicalpeak-to-peak amplitude as signal 90. As shown by FIG. 2B, the signal 96output by the inverter 77 has a clipped trough corresponding to theclipped peak of signal 94B, and the signal 96 has a positive peakcorresponding to the negative trough of signal 94B.

The signal 96 is provided from attenuator 79 (in the embodiment of FIG.2A) or inverter 77 (in the embodiment of FIG. 2B) to gain stage 88. Inthe simplified case of FIGS. 2A and 2B, the non-linear amplifier 88 hasthe same non-linear asymmetrical characteristic of non-linear amplifier80, e.g., by “clipping” the positive level of the output signal when thepositive level of the input signal reaches a specific amplitude. In thedepicted embodiment, the positive peak of the input signal to non-linearamplifier 88 is clipped in the same manner and level as the positivepeak of the input signal to non-linear amplifier 80. The resultingoutput signal from non-linear amplifier 88 has a positive clipped shapewhile leaving the negative trough substantially unchanged. In anembodiment, the first order and higher order gains applied by non-linearamplifier 88 may be substantially identical to those applied bynon-linear amplifier 80. In the simplified depiction of the signalportions of FIGS. 2A and 2B, this may be depicted as an increase in thepeak-to-peak amplitude of the input 96 as well as a substantiallyidentical clipping of the signal at its peak, resulting in an outputsignal 98. The output signal 98 may have a desired overall first ordergain (e.g., RF gain) applied to it while an undesired higher ordersignal portion (e.g., second order signal components) may be removedfrom the signal due to the recovered symmetrical shape.

The present disclosure has discussed non-linear and linear circuitstages, which may be embodied in a variety of different electricaland/or optical devices or components such as RF gain block amplifiers,semiconductor lasers and photodetectors. In an embodiment, thenon-linear circuit stages may be gain stages embodied in RF amplifiers.RF amplifiers may include components such as Mini-Circuits GVA-81+,Qorvo ECG008, Analog Devices ADL5610 and may have first and second ordergain characteristics such as 10 to 18 decibel (dB) first order gain andsecond order distortion in the range 40 to 55 dBm (OIP2). A linearcircuit stage may include a RF inverter and a RF attenuator such as aMini-Circuits TC1-1G2+ transformer and a Mini-Circuits LAT-12+attenuator having a loss of 12 dB that substantially matches the gain ofthe RF amplifier.

While it will be understood that the non-linear and linear circuitstages may be configured in a variety of manners and may include avariety of components in accordance with the present disclosure,additional embodiments of RF circuitry including gain and attenuationstages are described with respect to FIGS. 6 and 7.

FIGS. 3A and 3B depict illustrative schematic diagrams for circuits forapplying a gain and removing second order distortion in accordance withsome embodiments of the present disclosure. In the embodiments of FIGS.3A and 3B, the non-linear circuit stage 75 and the non-linear circuitstage 81 are gain stages that are implemented with RF amplifiers 80 and88 and linear circuit stage 76 is an attenuation stage that isimplemented with an RF attenuator 79. Collectively, these components mayfunction as an RF amplifier having a desired first order gain and secondorder RF distortion substantially removed from the signal. However, itwill be understood that similar functionality may be employed inapplications other than RF, and for additional purposes other thanapplying a desired first order gain (e.g., to perform other processingwith matched circuitry in a manner that reduces an undesired (e.g.,second order) distortion in an output signal.

In the embodiments of FIGS. 3A and 3B, the amplifier stage 75 may be aninverting RF amplifier (as shown by amplifier 80 and inverter 77) havinga first order gain and a second order distortion. An input signal may beamplified based on these gains and inverted, with the output signalbeing provided to the RF attenuator 79 of linear circuit stage 76. In anembodiment, the RF attenuator 79 may have a first order loss that issubstantially equal to the first order gain of the RF amplifier 80, suchthat the output signal from the RF attenuator 79 has a substantiallyunity gain of first order signal components with respect to the inputsignal to RF amplifier 80. The resulting signal that is output from theRF attenuator 79 may thus be inverted with respect to the input signalto RF amplifier 80 and may also have second order distortion as a resultof the processing of RF amplifier 80.

The output signal from attenuator 79 may be provided to the RF amplifier88 of non-linear circuit stage 81. The RF amplifier 88 may, in oneembodiment, have a similar first order gain and second order distortionto the RF amplifier 80. However, in other embodiments, the RF amplifier88 may have a different first order gain and second order distortionfrom the RF amplifier 80. In the embodiment of FIG. 3A, the non-linearcircuit stage 81 may not be inverting, while in the embodiment of FIG.3B, the non-linear circuit stage 81 may be configured as an inverting RFamplifier (with RF amplifier 88 and inverter 77). Accordingly, asdescribed herein, the application of the gains of RF amplifier 88 to theoutput signal of attenuator 79 may result in an output signal from RFamplifier 88 that has the first order gain that is substantially equalto the first order gain of RF amplifier 88, but has second order gaindistortion removed.

Note that circuits are generally designed to meet desired specificationswithin certain tolerances that can be selected based on various designconstraints or factors. The term “substantially,” when used to describea criterion of a parameter herein, refers to the parameter being within10% of the stated criterion. As an example, “substantially cancelling”second order harmonic distortions refers to reducing the second orderharmonic distortion by at least 10 dB. It has been shown that use of thetechniques described herein for amplifying signals can result in areduction of 10 to 20 dB of second order distortion.

Referring to the embodiment of FIG. 2, the explanation of the presentinvention has been simplified by neglecting to discuss the time delaypresent in coaxial cables and optical fibers. Provided that any delayelement preserves the phase relationship between the fundamental andsecond harmonic components in the frequency domain, the simplifiedexplanation still holds true. For example, if the non-linear stages bothclip the positive peaks of the waveform, it is not important whetherthey both clip the positive peaks at the same instant in time or not.

Methods for utilizing the linear and non-linear circuit stages to applydesired processing while removing undesired higher order signalcomponents from the output signal are depicted and described in FIGS.4-5. Although a particular order or flow of steps is depicted in FIGS.4-5, some operations may be performed in a different order, thatadditional steps may be added, or that one or more steps may be removed,as is describe herein or as may otherwise be understood by a personhaving ordinary skill in the art in view of the present disclosure.

FIG. 4 depicts an illustrative flow chart for a method of removingsecond order distortion in accordance with some embodiments of thepresent disclosure. In the embodiment of FIG. 4, series circuit stagesmay include a first non-linear circuit stage, a linear circuit stage,and a second non-linear circuit stage.

At step 402, an input signal may be provided to the first non-linearcircuit stage. Processing may continue to step 404, at which the firstnon-linear circuit stage may modify the input signal, for example, byapplying first order and higher order processing to the input signal. Insome embodiments, the processing of the first non-linear circuit stagemay invert the input signal. The resulting output signal may be providedto a linear circuit stage, and processing may continue to step 406.

At step 406, the linear circuit stage may process the signal that isreceived from the first non-linear circuit stage. In an embodiment, thelinear circuit stage may perform complementary first order processing tothe first non-linear circuit stage, such that the signal that is outputfrom the linear circuit stage may have substantially identical firstorder characteristics to the signal that input to the first non-linearcircuit stage. If the input signal to the first non-linear circuit stagewas not inverted at that stage, an inversion may be performed at thelinear circuit stage at step 406. The resulting signal may then beprovided to the second non-linear circuit stage, and processing may thencontinue to step 408.

At step 408, the second non-linear circuit stage may process thereceived signal. Although processing may be performed in a variety ofsuitable manners, in an embodiment the second non-linear circuit stagemay have substantially identical circuit characteristics (e.g., firstorder and higher order such as second order) as the first non-linearcircuit stage. With respect to the original input signal to the firstnon-linear circuit element, a desired first order signal modificationmay be applied to input signal. The output signal may not include anundesired higher order signal component (e.g., second order signalcomponent), which may be removed by the second non-linear circuit stage.Once the output signal with the desired first order signal modificationhas been processed and output by the second non-linear circuit stage,the processing of FIG. 4 may end.

FIG. 5 depicts an illustrative flow chart for a method of removingsecond order distortion in accordance with some embodiments of thepresent disclosure. In the embodiment of FIG. 5, the first non-linearcircuit stage and second non-linear circuit stage may be identical RFgain stages implemented with amplifiers, while the linear circuit stagemay include an inverter and RF attenuator, with the RF attenuator havinga first order loss that is substantially complementary to the firstorder gain of the RF amplifier of the first non-linear circuit stage.

Processing starts at step 502 when a first gain stage 75 receives asignal that is to be amplified. As an example, the signal may be awideband RF signal received from the base station 15 via one or morehubs 22 and 25 and optical fibers 39, as depicted in FIG. 6. As shown byblock 502 of FIG. 5, the first gain stage 75 applies a gain (G) to thesignal. In doing so, the first gain stage 75 may introduce non-lineardistortion, including in particular second order harmonic distortion,while also clipping a portion of the RF signal. Processing may thencontinue to step 504.

As shown by block 504 of FIG. 5, the signal processed by the first gainstage 75 is inverted. Processing then continues to step 506, at whichthe signal is attenuated in order to substantially remove the firstorder gain (G) applied to the signal by the first gain stage 75. Inanother embodiment, the attenuation of the signal at step 506 may occurbefore the inversion of the signal in step 504. The resulting signalthat is output from the attenuator is inverted with respect to theoriginal input signal, has second order distortion based on thedistortion from step 502, and has a substantially unity first ordergain. The output signal from the attenuator is provided to an amplifierof the second gain stage 81, and processing then continues to step 508.

At step 508, a second gain stage 81 having characteristics (e.g., gainand saturation levels) similar to the first gain stage 75 amplifies thesignal in order to apply the gain (G) removed by the attenuation inblock. Since the gain stages 75 and 81 have similar characteristics, thestages 75 and 81 distort the signal similarly. However, since the signalis inverted at the input of the gain stage 81 relative to the input ofthe gain stage 75, the stages 75 and 81 distort the peaks and troughssymmetrically such that the second gain stage 81 substantially cancelsthe second order harmonic distortion introduced by the first gain stage75 resulting in a signal at the output of the second gain stage 81 thatis substantially free of second order harmonic distortion and isamplified with a first order gain (G) relative to the signal at theinput of the first gain stage 75.

FIG. 6 depicts an embodiment of a communication system 100 having adistributed antenna system (DAS) 102 for wirelessly communicatingsignals between at least one base station (or network communicationdevice) 15 (e.g., a RF source or a millimeter wave (mmwave) source) andnumerous mobile communication devices 18. Such a system may be employedin a variety of applications, for example, where coverage bycommunication networks (e.g., cellular, WiFi, etc.) is limited or wherea high density of communication devices 18 are typically used andemployed, such as sporting venues, public squares, casinos, conventioncenters, hotels, and other similar venues. The DAS 102 of FIG. 6 has ahub 22, referred to herein as a “primary hub,” that may be coupled toone or more base stations 15 by one or more electrical and/or opticalconnections communicating respective electrical and/or optical signals.The base stations 15 may function as a gateway to one or more existingcommunications systems, such as the different cellular phone networks ofdifferent carriers, the internet, fiber optic networks, etc.

In an embodiment, the DAS 102 may facilitate communications between anumber of disparate networks that are accessible from base station 15and the disparate mobile communication devices 18 that operate on thosenetworks. Although DAS 102 may operate in a variety of manners (e.g., byproviding a plurality of communication paths for different devices tocommunicate with different networks), in an embodiment as describedherein the DAS 102 may function as a wideband DAS, that communicates RFsignals between the base station 15 and the mobile communication devices18 over a wide range of frequencies that are at least 1 octave apart,and in many embodiments, frequencies that are 1, 2, or greater orders ofmagnitude apart may be communicated, for example, in ranges such as 130MHz to 2.7 GHz, 130 MHz to 3.5 GHz, and 150 MHz to 6 GHz (e.g., toaccommodate any such signals in this range including the 5.9 GHz ISMband). In this manner, the DAS 102 may facilitate communications overmultiple different communication and network protocols over a single DAS102, with the underlying RF communication signals being communicatedover shared communication mediums without modification. In anembodiment, DAS 102 may provide for end-to-end communications betweenthe base station(s) 15 and the mobile communication devices, withoutperforming any RF modulation of the disparate RF signals that arecommunicated over differing networks and via differing protocols. Allcommunications may be routed through DAS 102 without RF modulation, forexample, via fiber optic communication links that employ optical signalmodulation between RF conversion stages, as described herein.

Returning to FIG. 6, the base station 15 may be coupled to a primary hub22 of DAS 102. The primary hub 22 may be coupled to at least one otherhub 25, referred to herein as a “secondary hub,” and a plurality ofremote units 33′. Together, the primary hub and secondary hubs may forma star network, with the primary hub functioning as a primary node andthe secondary hubs functioning as branch or peripheral nodes. Eachremote unit provides for a communication endpoint with mobile devices,e.g., via RF transmissions through an antenna of the remote units. Eachsecondary hub may provide for connections to additional remote units(33″ in FIG. 6) as well as additional secondary hubs. For simplicity ofillustration, FIG. 6 shows a single secondary hub 25. However, theprimary hub 22 may be interfaced with multiple secondary hubs 25, and asecondary hub 25 may be further interfaced with multiple additionalsecondary hubs 25 to form a DAS 102 of any desired size or scale (e.g.,as a two-star distributed antenna system). The secondary hubs 25 may inturn be coupled to additional remote units 33″, which allows DAS 102 tobe employed over large physical areas and for scalability to dozens oreven hundreds of remote units over unique physical environments.

In some embodiments, the primary hub 22 may be coupled to the secondaryhub 25 and the remote units 33′ by respective optical fibers 39, withoptical fibers 39′ corresponding to optical fiber connections betweenthe primary hub and other devices (e.g., remote units 33′ or secondaryhubs 25). In an embodiment, each optical fiber 39 may include aplurality (e.g., two) of fiber connections to provide different physicalfiber links for uplink and downlink communications over DAS 102. Inother embodiments, connections to remote units 33 by a hub or secondaryhub may be direct electrical connections, with optical connections onlyprovided between hub devices. In other embodiments, other types ofcommunication connections may be used. Indeed, it is possible for anycomponent of the DAS 102 to communicate with any other componentoptically, electrically, or wirelessly. However the signals arecommunicated through the DAS 102, the underlying RF communication signalneeds to be retained or reconstructed at both ends of the DAS 102, toenable communications with remote devices 18 and base station 15.Accordingly, as will be described in more detail hereafter, any of thecomponents of the DAS 102, such as the primary hub 22, secondary hub 25,and remote units 33, may employ RF amplifiers that amplify signals forRF communications. As described herein, these amplifiers may beconfigured and coupled in a manner that reduces undesired signalcharacteristics such as linear distortions (e.g., second order lineardistortion) on the output RF signal, which might otherwise occur duringgain stages.

In the downstream direction, the primary hub 22 may receive electricalsignals (e.g., multiple RF signals or other type of signal over awideband) to be communicated to different ones of mobile communicationdevices 18 (e.g., to different subscribers to different cellularnetworks). In an embodiment, the primary hub 22 includes multipleservice modules, processors, memories, and RF communication devices andswitches that facilitate the combination of the incoming RF traffic intocommon RF data, e.g., to combine and balance the mix of cellular servicesignals and other RF signals into one wideband composite RF signal. Theoutput RF data is provided to one or more optical modules of the hub,which modulate the RF signals for transmission as an optical signal overoptical fibers 39′. In an embodiment, the modulation of the RF signalsdoes not change the underlying RF signal, but instead, merely providesan optical carrier signal for the underlying RF signals withoutconversion into a digital signal. The resulting downstream opticalsignal is transmitted over the optical fibers 39′ (e.g., over a downlinkfiber of an optical fiber 39′). Although in an embodiment the samedownlink signal may be transmitted over each of the optical fibers 39′,in some embodiments different RF signals may be routed to differentremote units 33′ or secondary hubs 25 (e.g., based on knowledge and/orpredictions regarding the locations of various mobile communicationdevices 18 relative to components of the DAS 102).

A remote unit 33′ may receive the downlink signal (e.g., the opticalsignal including an optical carrier and the underlying RF signals) fromthe primary hub and output the underlying RF content received from thebase station 15 to the mobile devices 18 via a local antenna of theremote device. In an embodiment, the received optical signal may beconverted to the electrical domain, for example, by demodulating theoptical carrier to output the underlying RF electrical content. However,while the underlying RF signal may maintain its underlying content(e.g., relative frequency, phase, amplitude, etc.), as a result ofoptical transmission and conversion the signal may need to be amplifiedprior to transmission to the mobile communication devices 18. Asdescribed herein, a RF gain stage may amplify the signal fortransmission, in a manner that reduces the second order non-lineardistortion that RF amplifiers often impart on the amplified signal. Byreducing this second order non-linear distortion, this may provide for atransmitted signal from the remote unit 33′ that is free ofnon-compliant spurious emissions created at the sum and differencefrequencies of the individual RF carriers.

Each secondary hub 25 may include suitable processors, memory, hardware,and software to facilitate the distribution of the signals (e.g.,optical signals carrying RF content) throughout the DAS 102. In anembodiment, the secondary hub may include a plurality of optical modulesthat transmit or receive optical signals, with the receiving opticalmodules converting the incoming optical signal into a RF signal and thetransmitting optical modules converting RF signals into the outgoingoptical signal. Internal processing of the RF signals by the secondaryhub may in some instances require one or more gain stages. In otherembodiments, the secondary hub 25 may route optical systems betweenvarious locations, without intermediate RF conversion within thesecondary hub 25. In some embodiments, a secondary hub may perform someportion of functionality of a remote unit 33, for example, by providingfor transmission of an RF signal from antennas coupled directly tosecondary hub 25, or performing a conversion to RF signals and providingthe electrical RF signal to a remote unit 33.

Note that the system 100 may have components, such as repeaters (notshown) or networks (not shown), through which signals may becommunicated to extend the effective communication range between the DAS102 and the mobile communication devices 18. In addition, if the DAS 102has additional secondary hubs 25, the signal being communicateddownstream may be similarly converted from the optical domain to theelectrical domain at each secondary hub for wireless transmission of thesignal by remote units 33 coupled to the respective secondary hub.

In the upstream direction, the mobile communication devices 18 maywirelessly transmit an electrical signal (e.g., RF signal) to bereceived by the base station 15. Such signals may be received by any ofthe remote units 33′ or 33″ based on the location of the mobilecommunication devices relative to the remote units 33′ or 33″. In anembodiment in which the remote units communicate with hubs via opticalcommunications, a RF signal received by a remote unit 33″ may beconverted to the optical domain and transmitted to the secondary hub 25via an uplink fiber of optical fibers 39″. The optical fibers may thenprovide the optical signal to the primary hub 22 via an uplink fiber ofoptical fiber 39′. Remote units 33′ may provide their received RFsignals directly to primary hub 22 via uplink fibers of optical fibers39′. The primary hub 22 may then convert the optical signal to a RFelectrical signal for transmission of the electrical signal to the basestation 15, which may require one or more RF amplification stages. Thebase station 15 may then provide the output RF signals to the targetcommunication networks (e.g., by distinguishing and selectivelydistributing via different bands and communication protocols).

FIG. 7 depicts an embodiment of a remote unit 33 in accordance with someembodiments of the present disclosure. Although a remote unit 33 maysend and receive signals to one or more hubs or other devices via avariety of transmission mediums (e.g., optical, electrical, wireless,etc.), in an embodiment the remote unit 33 may communicate with hubs viaoptical fibers. Although remote unit 33 may include different hardwarein order to communicate via different transmission mediums, and utilizedifferent hardware and software for each transmission medium, in anembodiment the remote unit 33 may communicate via optical fibers and mayinclude an optical module 52, RF gain stage 54, power gain stage 56,electrical communication path 57, and may be coupled to an antenna 58.

Optical module 52 may be coupled to the optical fiber 39. In anembodiment, optical module 52 may be coupled to separate downlink anduplink fibers 39, such that optical module 52 (or, in some embodiments,multiple optical modules) provides parallel processing of downlinktraffic (e.g., requiring optical to electrical conversion from the hubto the antenna) and uplink traffic (e.g., requiring electrical tooptical conversion to the hub from the antenna). For the downlinksignal, the optical module 52 may detect the envelope of an opticalcarrier signal and output the wideband of RF signals to a RF gain stage54 without modulation of the underlying RF signals. For the uplinksignal, the RF signals may be provided to the optical module 52 from theRF gain stage 54 as a wideband of RF signals, and the optical module 52may apply conversion to the optical domain by applying intensitymodulation to an optical carrier signal, providing the resulting opticalsignal to the uplink fiber of optical fiber 39.

RF gain stage 54 may apply a RF gain to the RF signals that areexchanged between the optical modules 52 and the antennas 58 (e.g., viapower amplifier 56 and electrical communication path 57). In anembodiment as described in more detail herein, the RF gain stage 54 mayemploy techniques to apply a significant (e.g., 5×, 10×, 20×, 50×) gainto the RF signal received from either the optical module 52 or antenna58, while avoiding non-linear distortions (e.g., second order non-lineardistortions) from be applied to the RF signals by the amplifiers of thegain stage. Moreover, while the RF gain stage is described herein asbeing employed at the remote unit 33, it will be understood that the RFgain stage as described herein may be employed at any suitable stage ofa system (e.g., electrical, optical, wireless, etc.) at which RF signalsneed to be amplified, for example, at each of hub 22 and secondary hubs,wherein conversion between optical and electrical signals occurs.

Power amplifier 56, electrical communication path 57, and antenna 58 mayprovide for the wideband wireless communication interface with themobile communication devices 18. Power amplifier may accommodate theentire wideband as described herein, providing amplification oftransmitted and received signals to and from the antenna (e.g.,transmitted and received via a coaxial cable or other similar electricalcommunication path 57) from a variety of carriers and utilizing a numberof different communication protocols, as described herein. In thismanner, multiple different mobile communication devices within thephysical range of the power amplifier 56 and antenna 58 may transmit andreceive communications over their communication networks via DAS 102.

FIG. 8 depicts an embodiment of an optical module 52 (e.g., of a remoteunit 33, primary hub 22, or secondary hub 25). The optical module 52 ofFIG. 8 has an optical receiver 66 that is coupled to a downlink fiber ofan optical fiber, such as downlink fiber 39D of the optical fiber 39that is also coupled to the primary hub 22. The optical receiver 66 isconfigured to receive an optical signal carried by the fiber 39 andconvert this signal from the optical domain to the electrical domain. Asan example, the optical receiver 66 may include an avalanche photodiode(APD) and associated circuitry for biasing the APD so that the APD has adesired sensitivity for appropriately converting the optical signal toan electrical signal depending on the expected characteristics, such asreceived signal strength, of the optical signal.

The electrical signal that is output by the optical receiver 66 may beprovided to conversion circuitry 67. In an embodiment, conversioncircuitry 67 may remove signal content that was added to the underlyingRF signal for optical transmission, such as an optical carrier signal.The resulting RF signal may be output for eventual transmission for anantenna, e.g., to a gain stage 54 that amplifies the received electricalsignal received via the optical receiver 66, thereby providing a gain(G) to such signal. As will be described in more detail hereafter, thegain stage 54 has circuitry (e.g., one or more RF power amplifiers) foramplifying an electrical signal, and the gain stage 54 processes thereceived electrical signal in a manner that eliminates second orderharmonic distortion without requiring complex circuitry such as parallelamplifier paths.

Note that each of the optical modules 52 may also have an opticaltransmitter 68 and conversion circuitry 69 similar to the opticalreceiver 66 and conversion circuitry 67 in the upstream direction,applying an optical carrier to an electrical signal and converting theelectrical signal to an optical signal. Similarly, there will beelectrical to optical conversions in the downlink path (e.g., at a hubproviding an optical signal to another hub or to a remote unit) andoptical to electrical conversions in the downlink path (e.g., at a hubreceiving an optical signal from another hub or from a remote unit).

The foregoing is merely illustrative of the principles of thisdisclosure and various modifications may be made by those skilled in theart without departing from the scope of this disclosure. The abovedescribed embodiments are presented for purposes of illustration and notof limitation. The present disclosure also can take many forms otherthan those explicitly described herein. Accordingly, it is emphasizedthat this disclosure is not limited to the explicitly disclosed methods,systems, and apparatuses, but is intended to include variations to andmodifications thereof, which are within the spirit of the followingclaims.

As a further example, variations of apparatus or process parameters(e.g., dimensions, configurations, components, process step order, etc.)may be made to further optimize the provided structures, devices andmethods, as shown and described herein. In any event, the structures anddevices, as well as the associated methods, described herein have manyapplications. Therefore, the disclosed subject matter should not belimited to any single embodiment described herein, but rather should beconstrued in breadth and scope in accordance with the appended claims.

What is claimed is:
 1. A method for reducing second-order non-lineardistortion in a wideband system, the method comprising: receiving aninput signal at a first non-linear circuit stage, wherein the firstnon-linear circuit stage applies an initial second-order non-linearmodification having an initial second-order distortion to the inputsignal to provide a first non-linear signal; providing the firstnon-linear signal to one or more intermediate circuit stages, whereinthe one or more intermediate circuit stages apply at least a linearmodification to the first non-linear signal to generate a modifiednon-linear signal, and wherein the modified non-linear signal isinverted with respect to the input signal; and providing the modifiednon-linear signal to a second non-linear circuit stage, wherein thesecond non-linear circuit stage applies an additional second-ordernon-linear modification having an additional second-order distortion tothe modified non-linear signal to output an output signal, wherein theone or more intermediate circuit stages have an overall transferfunction that results in second-order distortion being substantiallyremoved from the output signal.
 2. The method of claim 1, wherein theinitial second-order non-linear modification has an initial first ordercomponent, the additional second-order non-linear modification has anadditional first order component and the linear modification has anattenuation factor with an intermediate first order component.
 3. Themethod of claim 2, wherein the initial second-order distortion and theadditional second-order distortion are substantially identical.
 4. Themethod of claim 3, wherein the initial first order component, theadditional first order component and the intermediate first ordercomponent are substantially equal.
 5. The method of claim 2, wherein: afirst ratio of the initial second-order distortion and the initial firstorder component is substantially equal to a second ratio of theadditional second-order distortion and the additional first ordercomponent; and the initial first order component is substantially equalto the intermediate first order component.
 6. The method of claim 5,wherein the initial first order component is not equal to the additionalfirst order component.
 7. The method of claim 2, wherein: a first ratioof the initial second-order distortion and the initial first ordercomponent is not equal to a second ratio of the additional second-orderdistortion and the additional first order component; and theintermediate first order component is based on the initial first ordercomponent, the additional first order component, the initialsecond-order distortion and the additional second-order distortion. 8.The method of claim 1, wherein the two non-linear circuit stages providesignal amplification and the one or more intermediate stages providesignal attenuation.
 9. The method of claim 1, wherein the two non-linearcircuit stages provide signal attenuation and the one or moreintermediate stages provide signal amplification.
 10. The method ofclaim 1, wherein the total gain applied to the input signal by the firstnon-linear circuit stage and the one or more intermediate circuit stagesis substantially equal to unity.
 11. A distributed antenna systemcomprising: a gain stage configured to apply a gain to a signalcommunicated by the distributed antenna system, the gain stagecomprising: a first non-linear circuit stage, wherein the firstnon-linear circuit stage applies an initial second-order non-linearmodification having an initial second-order distortion to an inputsignal to provide a first non-linear signal; one or more intermediatecircuit stages coupled to the first non-linear circuit stage to receivethe first non-linear signal, wherein the one or more intermediatecircuit stages apply at least a first order modification to the firstnon-linear signal to generate a modified non-linear signal, and whereinthe modified non-linear signal is inverted with respect to the inputsignal; and a second non-linear circuit stage coupled to one of the oneor more intermediate circuit stages to receive the modified non-linearsignal, wherein the second non-linear circuit stage applies anadditional second-order non-linear modification having an additionalsecond-order distortion to the modified non-linear signal to output anoutput signal, wherein the one or more intermediate circuit stages havean overall transfer function that results in second-order distortionbeing substantially removed from the output signal.
 12. The system ofclaim 11, wherein: the initial second-order non-linear modification hasan initial first order component, the additional second-order non-linearmodification has an additional first order component and the first ordermodification has an attenuation factor with an intermediate first ordercomponent; the initial second-order distortion and the additionalsecond-order distortion are substantially identical; and the initialfirst order component, the additional first order component and theintermediate first order component are substantially equal.
 13. Thesystem of claim 11, wherein: the initial second-order non-linearmodification has an initial first order component, the additionalsecond-order non-linear modification has an additional first ordercomponent and the first order modification has an attenuation factorwith an intermediate first order component; a first ratio of the initialsecond-order distortion and the initial first order component issubstantially equal to a second ratio of the additional second-orderdistortion and the additional first order component; and the initialfirst order component is substantially equal to the intermediate firstorder component.
 14. The system of claim 11, wherein: the initialsecond-order non-linear modification has an initial first ordercomponent, the additional second-order non-linear modification has anadditional first order component and the first order modification has anattenuation factor with an intermediate first order component; a firstratio of the initial second-order distortion and the initial first ordercomponent is not equal to a second ratio of the additional second-orderdistortion and the additional first order component; and theintermediate first order component is based on the initial first ordercomponent, the additional first order component, the initialsecond-order distortion and the additional second-order distortion. 15.The system of claim 11, wherein the first non-linear circuit stage, oneor more intermediate circuit stages, or second non-linear circuit stagecomprise one of optical components or electrical components.
 16. Thesystem of claim 11, further comprising a hub and a remote unit, whereinthe first non-linear stage is located in the hub and the secondnon-linear stage is located in the remote unit.
 17. The system of claim11, wherein the first non-linear circuit stage and the second non-linearcircuit stage each comprise an inverting amplifier.
 18. The system ofclaim 17, further comprising a hub, wherein the hub includes each of thefirst non-linear circuit stage, one or more intermediate circuit stages,and second non-linear circuit stage.
 19. The system of claim 17, furthercomprising a remote unit, wherein the remote unit includes each of thefirst non-linear circuit stage, one or more intermediate circuit stages,and second non-linear circuit stage.
 20. The system of claim 11, furthercomprising: a primary hub connected to a secondary hub; each of thefirst non-linear circuit stage and the second non-linear stage includesone or more optical elements; and each of the first non-linear circuitstage and the second non-linear stage are located at one of the primaryhub and the secondary hub.
 21. The system of claim 11, wherein theinversion of the modified non-linear signal is provided by one of aninverter, transformer or crossover of differential connections.
 22. Thesystem of claim 11, wherein the substantial removal of second-orderdistortion from the output signal includes the removal of second-orderharmonics and second-order intermodulation products.
 23. A system forreducing second-order distortion in a wideband system, the systemcomprising: a first non-linear circuit stage, wherein the firstnon-linear circuit stage applies an initial second-order non-lineartransfer function having an initial second-order distortion to an inputsignal to provide a first non-linear signal; one or more intermediatecircuit stages coupled to the first non-linear circuit stage to receivethe first non-linear signal, wherein the one or more intermediatecircuit stages apply at least a first order transfer function to thefirst non-linear signal to generate a modified non-linear signal; and asecond non-linear circuit stage coupled to one of the one or moreintermediate circuit stages to receive the modified non-linear signal,wherein the second non-linear circuit stage applies an additionalsecond-order non-linear transfer function having an additionalsecond-order distortion to the modified non-linear signal to output anoutput signal, the additional second-order distortion being differentfrom the initial second-order distortion, wherein the first non-linearcircuit stage, one or more intermediate circuit stages, and secondnon-linear circuit stage produce an overall second-order distortion inthe output signal that is lower than the either of the initialsecond-order distortion and the additional second-order distortion. 24.The system of claim 23, wherein: the initial second-order non-lineartransfer function has an initial first order component, the additionalsecond-order non-linear transfer function has an additional first ordercomponent and the first order transfer function has an attenuationfactor with an intermediate first order component; a first ratio of theinitial second-order distortion and the initial first order component issubstantially equal to a second ratio of the additional second-orderdistortion and the additional first order component; and the initialfirst order component is substantially equal to the intermediate firstorder component.
 25. The system of claim 23, wherein: the initialsecond-order non-linear transfer function has an initial first ordercomponent, the additional second-order non-linear transfer function hasan additional first order component and the first order transferfunction has an attenuation factor with an intermediate first ordercomponent; a first ratio of the initial second-order distortion and theinitial first order component is not equal to a second ratio of theadditional second-order distortion and the additional first ordercomponent; and the intermediate first order component is substantiallyequal to a ratio of the initial first order component squared times theadditional second-order distortion and the additional first ordercomponent times the initial second-order distortion.